# How do you simplify (-5+6i)/(5+4i)?

Jan 13, 2016

#### Answer:

$\frac{- 1 + 50 i}{41}$

#### Explanation:

The automatic response is to try change the denominator such that it is no longer of type Complex. We do this by using what is called its 'Conjugate'. That is: $5 - 4 i$.

To do this we multiply the whole by the value of 1 but in the form of

$\frac{5 - 4 i}{5 - 4 i}$ so that we do not effectively change the value of the whole.
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$\frac{- 5 + 6 i}{5 + 4 i} \times \frac{5 - 4 i}{5 - 4 i}$

$\frac{- 25 + 20 i + 30 i - 24 {i}^{2}}{25 - 20 i + 20 i - 16 {i}^{2}}$

But ${i}^{2} = - 1$ giving:

$\frac{- 1 + 50 i}{41}$